%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU127+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:14:50 EDT 2022
% Result : Theorem 1.81s 2.07s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 8 unt; 1 nHn; 8 RR)
% Number of literals : 15 ( 3 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( subset(A,B)
| ~ in(dollar_f1(A,B),B) ),
file('SEU127+1.p',unknown),
[] ).
cnf(5,axiom,
( A != set_intersection2(B,C)
| ~ in(D,A)
| in(D,C) ),
file('SEU127+1.p',unknown),
[] ).
cnf(9,axiom,
~ subset(set_intersection2(dollar_c4,dollar_c3),dollar_c4),
file('SEU127+1.p',unknown),
[] ).
cnf(20,axiom,
A = A,
file('SEU127+1.p',unknown),
[] ).
cnf(21,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SEU127+1.p',unknown),
[] ).
cnf(22,axiom,
( subset(A,B)
| in(dollar_f1(A,B),A) ),
file('SEU127+1.p',unknown),
[] ).
cnf(56,plain,
~ subset(set_intersection2(dollar_c3,dollar_c4),dollar_c4),
inference(para_from,[status(thm),theory(equality)],[21,9]),
[iquote('para_from,21.1.1,9.1.1')] ).
cnf(107,plain,
in(dollar_f1(set_intersection2(dollar_c3,dollar_c4),dollar_c4),set_intersection2(dollar_c3,dollar_c4)),
inference(hyper,[status(thm)],[22,56]),
[iquote('hyper,22,56')] ).
cnf(928,plain,
in(dollar_f1(set_intersection2(dollar_c3,dollar_c4),dollar_c4),dollar_c4),
inference(hyper,[status(thm)],[107,5,20]),
[iquote('hyper,107,5,20')] ).
cnf(1108,plain,
subset(set_intersection2(dollar_c3,dollar_c4),dollar_c4),
inference(hyper,[status(thm)],[928,3]),
[iquote('hyper,928,3')] ).
cnf(1109,plain,
$false,
inference(binary,[status(thm)],[1108,56]),
[iquote('binary,1108.1,56.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU127+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 07:06:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.93 ----- Otter 3.3f, August 2004 -----
% 1.71/1.93 The process was started by sandbox on n017.cluster.edu,
% 1.71/1.93 Wed Jul 27 07:06:03 2022
% 1.71/1.93 The command was "./otter". The process ID is 20218.
% 1.71/1.93
% 1.71/1.93 set(prolog_style_variables).
% 1.71/1.93 set(auto).
% 1.71/1.93 dependent: set(auto1).
% 1.71/1.93 dependent: set(process_input).
% 1.71/1.93 dependent: clear(print_kept).
% 1.71/1.93 dependent: clear(print_new_demod).
% 1.71/1.93 dependent: clear(print_back_demod).
% 1.71/1.93 dependent: clear(print_back_sub).
% 1.71/1.93 dependent: set(control_memory).
% 1.71/1.93 dependent: assign(max_mem, 12000).
% 1.71/1.93 dependent: assign(pick_given_ratio, 4).
% 1.71/1.93 dependent: assign(stats_level, 1).
% 1.71/1.93 dependent: assign(max_seconds, 10800).
% 1.71/1.93 clear(print_given).
% 1.71/1.93
% 1.71/1.93 formula_list(usable).
% 1.71/1.93 all A (A=A).
% 1.71/1.93 all A B (in(A,B)-> -in(B,A)).
% 1.71/1.93 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.71/1.93 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.71/1.93 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.71/1.93 $T.
% 1.71/1.93 $T.
% 1.71/1.93 empty(empty_set).
% 1.71/1.93 all A B (set_intersection2(A,A)=A).
% 1.71/1.93 exists A empty(A).
% 1.71/1.93 exists A (-empty(A)).
% 1.71/1.93 all A B subset(A,A).
% 1.71/1.93 -(all A B subset(set_intersection2(A,B),A)).
% 1.71/1.93 all A (set_intersection2(A,empty_set)=empty_set).
% 1.71/1.93 all A (empty(A)->A=empty_set).
% 1.71/1.93 all A B (-(in(A,B)&empty(B))).
% 1.71/1.93 all A B (-(empty(A)&A!=B&empty(B))).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 -------> usable clausifies to:
% 1.71/1.93
% 1.71/1.93 list(usable).
% 1.71/1.93 0 [] A=A.
% 1.71/1.93 0 [] -in(A,B)| -in(B,A).
% 1.71/1.93 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.71/1.93 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.71/1.93 0 [] subset(A,B)|in($f1(A,B),A).
% 1.71/1.93 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.71/1.93 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.71/1.93 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.71/1.93 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.71/1.93 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A).
% 1.71/1.93 0 [] C=set_intersection2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),B).
% 1.71/1.93 0 [] C=set_intersection2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A)| -in($f2(A,B,C),B).
% 1.71/1.93 0 [] $T.
% 1.71/1.93 0 [] $T.
% 1.71/1.93 0 [] empty(empty_set).
% 1.71/1.93 0 [] set_intersection2(A,A)=A.
% 1.71/1.93 0 [] empty($c1).
% 1.71/1.93 0 [] -empty($c2).
% 1.71/1.93 0 [] subset(A,A).
% 1.71/1.93 0 [] -subset(set_intersection2($c4,$c3),$c4).
% 1.71/1.93 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.71/1.93 0 [] -empty(A)|A=empty_set.
% 1.71/1.93 0 [] -in(A,B)| -empty(B).
% 1.71/1.93 0 [] -empty(A)|A=B| -empty(B).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.71/1.93
% 1.71/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.93 deletion, with positive clauses in sos and nonpositive
% 1.71/1.93 clauses in usable.
% 1.71/1.93
% 1.71/1.93 dependent: set(knuth_bendix).
% 1.71/1.93 dependent: set(anl_eq).
% 1.71/1.93 dependent: set(para_from).
% 1.71/1.93 dependent: set(para_into).
% 1.71/1.93 dependent: clear(para_from_right).
% 1.71/1.93 dependent: clear(para_into_right).
% 1.71/1.93 dependent: set(para_from_vars).
% 1.71/1.93 dependent: set(eq_units_both_ways).
% 1.71/1.93 dependent: set(dynamic_demod_all).
% 1.71/1.93 dependent: set(dynamic_demod).
% 1.71/1.93 dependent: set(order_eq).
% 1.71/1.93 dependent: set(back_demod).
% 1.71/1.93 dependent: set(lrpo).
% 1.71/1.93 dependent: set(hyper_res).
% 1.71/1.93 dependent: set(unit_deletion).
% 1.71/1.93 dependent: set(factor).
% 1.71/1.93
% 1.71/1.93 ------------> process usable:
% 1.71/1.93 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.71/1.93 ** KEPT (pick-wt=9): 2 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.71/1.93 ** KEPT (pick-wt=8): 3 [] subset(A,B)| -in($f1(A,B),B).
% 1.71/1.93 ** KEPT (pick-wt=11): 4 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.71/1.93 ** KEPT (pick-wt=11): 5 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.71/1.93 ** KEPT (pick-wt=14): 6 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.71/1.93 ** KEPT (pick-wt=23): 7 [] A=set_intersection2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B)| -in($f2(B,C,A),C).
% 1.71/1.93 ** KEPT (pick-wt=2): 8 [] -empty($c2).
% 1.71/1.93 ** KEPT (pick-wt=5): 9 [] -subset(set_intersection2($c4,$c3),$c4).
% 1.71/1.93 ** KEPT (pick-wt=5): 10 [] -empty(A)|A=empty_set.
% 1.71/1.93 ** KEPT (pick-wt=5): 11 [] -in(A,B)| -empty(B).
% 1.71/1.93 ** KEPT (pick-wt=7): 12 [] -empty(A)|A=B| -empty(B).
% 1.71/1.93
% 1.71/1.93 ------------> process sos:
% 1.71/1.93 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.71/1.93 ** KEPT (pick-wt=7): 21 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.71/1.93 ** KEPT (pick-wt=8): 22 [] subset(A,B)|in($f1(A,B),A).
% 1.71/1.93 ** KEPT (pick-wt=17): 23 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B).
% 1.71/1.93 ** KEPT (pick-wt=17): 24 [] A=set_intersection2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),C).
% 1.71/1.93 ** KEPT (pick-wt=2): 25 [] empty(empty_set).
% 1.81/2.07 ** KEPT (pick-wt=5): 26 [] set_intersection2(A,A)=A.
% 1.81/2.07 ---> New Demodulator: 27 [new_demod,26] set_intersection2(A,A)=A.
% 1.81/2.07 ** KEPT (pick-wt=2): 28 [] empty($c1).
% 1.81/2.07 ** KEPT (pick-wt=3): 29 [] subset(A,A).
% 1.81/2.07 ** KEPT (pick-wt=5): 30 [] set_intersection2(A,empty_set)=empty_set.
% 1.81/2.07 ---> New Demodulator: 31 [new_demod,30] set_intersection2(A,empty_set)=empty_set.
% 1.81/2.07 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 1.81/2.07 20 back subsumes 18.
% 1.81/2.07 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.81/2.07 >>>> Starting back demodulation with 27.
% 1.81/2.07 >> back demodulating 19 with 27.
% 1.81/2.07 >> back demodulating 17 with 27.
% 1.81/2.07 >> back demodulating 14 with 27.
% 1.81/2.07 >>>> Starting back demodulation with 31.
% 1.81/2.07
% 1.81/2.07 ======= end of input processing =======
% 1.81/2.07
% 1.81/2.07 =========== start of search ===========
% 1.81/2.07
% 1.81/2.07 -------- PROOF --------
% 1.81/2.07
% 1.81/2.07 ----> UNIT CONFLICT at 0.14 sec ----> 1109 [binary,1108.1,56.1] $F.
% 1.81/2.07
% 1.81/2.07 Length of proof is 4. Level of proof is 4.
% 1.81/2.07
% 1.81/2.07 ---------------- PROOF ----------------
% 1.81/2.07 % SZS status Theorem
% 1.81/2.07 % SZS output start Refutation
% See solution above
% 1.81/2.07 ------------ end of proof -------------
% 1.81/2.07
% 1.81/2.07
% 1.81/2.07 Search stopped by max_proofs option.
% 1.81/2.07
% 1.81/2.07
% 1.81/2.07 Search stopped by max_proofs option.
% 1.81/2.07
% 1.81/2.07 ============ end of search ============
% 1.81/2.07
% 1.81/2.07 -------------- statistics -------------
% 1.81/2.07 clauses given 42
% 1.81/2.07 clauses generated 2952
% 1.81/2.07 clauses kept 1103
% 1.81/2.07 clauses forward subsumed 1872
% 1.81/2.07 clauses back subsumed 27
% 1.81/2.07 Kbytes malloced 2929
% 1.81/2.07
% 1.81/2.07 ----------- times (seconds) -----------
% 1.81/2.07 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 1.81/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.81/2.07
% 1.81/2.07 That finishes the proof of the theorem.
% 1.81/2.07
% 1.81/2.07 Process 20218 finished Wed Jul 27 07:06:05 2022
% 1.81/2.07 Otter interrupted
% 1.81/2.07 PROOF FOUND
%------------------------------------------------------------------------------